lateralContact2010 - Tribol Lett DOI...

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ORIGINAL PAPER Lateral Contact Stiffness and the Elastic Foundation Daniel J. Dickrell III W. G. Sawyer Received: 2 July 2009 / Accepted: 12 July 2010 Ó Springer Science+Business Media, LLC 2010 Abstract A model for the lateral contact stiffness for an elastic foundation was developed. The model was evaluated using a low force and low contact pressure microtribometer capable of performing indentation and reciprocated sliding experiments. The slope of lateral force versus the lateral displacement was used to Ft the shear modulus. When complementary elastic indentation mea- surements are made to determine the composite modulus of the elastic foundation, there is sufFcient data to Ft elastic modulus, shear modulus, and Poisson ratio for these thin Flms. Using these models, the elastic properties for a thin ( * 65 l m) vertically aligned multiwall carbon nanotube Flm were evaluated. The experiments were performed with a silicon nitride indenter (radius = 1.6 mm) over a range in loads from 100 to 800 l N. The resulting values of the elastic modulus, shear modulus, and Poisson ratio were E = 429 kPa, G = 156 kPa, and m = 0.37, respectively. Keywords Contact mechanics ± Elastic foundation ± Carbon nanotubes ± Nanotribology List of symbols A c Contact area b Contact radius C Resistance to deformation d Indentation depth D x Lateral deformation E Elastic modulus E 0 Composite elastic modulus F f ±riction force F n Normal force G Shear modulus k c Lateral contact stiffness m Poisson’s ratio R Indenter radius t Thickness 1 Introduction Lateral contact stiffness [ 1 ] has emerged as a powerful tool in the studies of contact, adhesion, and friction in the atomic force microscopy area [ 1 3 ]. In atomic scale research activities, it is typical to model the nanometer- sized contacts using continuum mechanics and linear elasticity. The limitations of using classical contact mechanics as the contact length scales approach atomic dimensions are a very active area of research that has been discussed in detail by Luan and Robbins [ 4 ]. Although there is uncertainty regarding the true contact area in nanotribological contacts, the ability to quantify lateral contact stiffness provides insights into the mechanics of thin Flms and is a useful tool in studies of contact, adhe- sion, and friction. Our interests in extending this technique to thin elastic layers at the macroscopic level were twofold: (1) to develop the mathematics for lateral contact stiffness of thin Flms and elastic layers, and (2) to explore the use of lateral contact stiffnesses in macroscopic tribological contacts as a technique to characterize such surfaces. There is a continuing interest in modeling and evaluat- ing contact, adhesion, and the friction of thin compliant layers. In the context of nanotribology, self-assembled monolayers are widely used as thin soft-layers to provide lubrication [ 5 ]. In macroscopic tribology the transfer Flms D. J. Dickrell III ± W. G. Sawyer ( & ) Department of Mechanical and Aerospace Engineering, University of ±lorida, Gainesville, ±L 32611, USA e-mail: [email protected]².edu
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This note was uploaded on 08/22/2011 for the course EGM 4313 taught by Professor Mei during the Spring '08 term at University of Florida.

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lateralContact2010 - Tribol Lett DOI...

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